WHERE DO BEST IDEAS COME FROM?
THE EMERGENCE OF MOST VALUABLE IDEAS IN SOCIAL STRUCTURES

Disaggregated results
Online Appendix
September, 2023

1. Results by Network

Table OA1. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Social Network and ss-max.
	Actor chooses max performing idea (ss-max = TRUE)										Actor chooses better performing idea (ss-max = FALSE)
	Small World I		Small World II		Small World III		Random		Fully-Connected		Small World I		Small World II		Small World III		Random		Fully-Connected
	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain activity	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)
Within-network-community recombination	1.97	-8.00	1.79	-8.51	1.83	-6.95					0.58	-2.60	0.78	-2.85	0.61	-2.74
Between-network-community recombination	3.43	-6.10	2.29	-5.98	2.25	-5.04					1.79	-1.23	1.10	-1.66	0.98	-1.96
Within-network-community transfer	-0.61	-0.40ns	-0.69	0.62	-0.50	0.08					-0.55	0.19	-0.39	0.85	-0.30	0.85
Between-network-community transfer	0.73	4.63	0.47ns	4.68	-0.12	4.10					0.64	5.19	-0.15	3.63	-0.11	3.00
Self-search	-1.18	17.01	-1.09	17.05	-1.16	16.76	-0.83	16.85	-0.76	15.84	-0.25	8.00	-0.37	7.36	-0.25	7.13	-0.25	7.81	-0.18	6.93
Recombination							1.52	-6.21	0.96	-4.45							0.67	-2.06	0.36	-1.48
Transfer							-0.31	2.23	-0.11	1.79							-0.15	0.94	-0.03	1.14
No. of observations (chains)	36,905	16,921	37,029	17,273	36,956	17,515	37,127	17,203	37,184	18,968	37,007	20,147	37,111	20,309	36,989	20,782	36,995	20,295	37,075	22,059
Notes:
nsEstimated coefficients are not statistically significant at the 95% confidence level
Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.
Recombinations and transfers cannot be disaggregated by between- and within-network community in random and fully-connected networks because these network structures do not have network communities.
Estimations made using data from 50,000 runs for each network and ss-max condition (5,000 runs by lanscape). All runs used parameters collab = 0.8 and recomb = 0.8.

2. Results by Landscape

Table OA2. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Landscape and ss-max.
	Actor chooses max performing idea (ss-max = TRUE)
	Custom landscape		N=8, K=2		N=8, K=4		N=8, K=6		N=10, K=2		N=10, K=4		N=10, K=6		N=12, K=2		N=12, K=4		N=12, K=6
	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain activity	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)
Within-network-community recombination	1.14	-6.39	2.88	-5.25	3.91	-9.85	3.35	-9.23	2.02	-6.32	2.30	-8.44	2.18	-8.68	1.44	-4.71	1.70	-6.33	1.47	-10.14
Between-network-community recombination	2.49	-2.72	3.35	-5.88	4.37	-4.44	3.14	-10.99	2.73	-5.50	2.93	-5.73	2.15	-9.51	2.90	-2.94	2.60	-3.95	2.03	-6.41
Within-network-community transfer	-0.45	0.39ns	-1.09	1.35	-0.72	1.53	-0.74	-1.55	-0.73	0.62	-0.73	0.23	-0.54	0.46	-0.58	-1.02	-0.46	-1.00	-0.47	-0.64
Between-network-community transfer	0.92	3.05	-0.08ns	3.94	-1.10	0.94	-0.62	1.13	0.45	4.63	0.12	3.39	0.11	1.40	0.63	3.69	0.55	5.04	0.36	0.22
Self-search	-1.06	8.03	-1.79	14.81	-2.29	30.79	-1.93	22.28	-1.53	19.48	-1.53	19.48	-1.29	26.10	-1.29	14.97	-1.26	16.92	-0.90	19.98
No. of observations (chains)	21,741	6,324	12,677	13,922	17,793	9,155	21,577	4,832	13,763	13,449	18,890	8,515	21,996	4,652	14,718	13,066	19,677	8,149	22,645	4,024

	Actor chooses better performing idea (ss-max = FALSE)
	Custom landscape		N=8, K=2		N=8, K=4		N=8, K=6		N=10, K=2		N=10, K=4		N=10, K=6		N=12, K=2		N=12, K=4		N=12, K=6
	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain activity	(21)	(22)	(23)	(24)	(25)	(26)	(27)	(28)	(29)	(30)	(31)	(32)	(33)	(34)	(35)	(36)	(37)	(38)	(39)	(40)
Within-network-community recombination	0.77	-3.28	0.55	-3.03	1.33	-3.86	1.36	-5.44	0.13ns	-1.59	0.37	-1.75	0.77	-1.62	0.21ns	-1.30	0.35	-1.97	0.69	-1.97
Between-network-community recombination	2.64	-1.52	0.51ns	-1.74	0.94	-1.86	1.44	-0.59ns	0.47	-1.81	0.97	-0.92ns	1.11	-1.24ns	0.77	-1.37	0.86	-0.51ns	1.14	-1.70
Within-network-community transfer	-0.35	0.53ns	-0.95	1.10	-1.01	1.02ns	-0.79	0.74ns	-0.38	0.19ns	-0.33	-0.22ns	-0.76	0.45ns	-0.45	0.70	-0.28	0.05ns	-0.37	0.99ns
Between-network-community transfer	0.96	6.24	-0.28ns	3.65	-0.94	2.07ns	0.07ns	0.63ns	0.57ns	2.34	-0.11ns	1.85ns	-0.08ns	0.60ns	0.05ns	2.80	-0.41ns	3.41	-0.07ns	1.64ns
Self-search	-0.84	4.74	-0.11ns	11.96	-0.19ns	12.24	-0.39	14.37	-0.21	8.14	-0.14ns	8.24	-0.21	8.82	-0.22	5.43	-0.19	6.91	-0.30	6.70
No. of observations (chains)	21,581	7,319	12,782	15,202	17,939	10,482	21,597	5,826	13,680	15,283	18,763	10,582	22,074	6,001	14,595	15,191	19,670	10,424	22,597	5,810
Notes:
nsEstimated coefficients are not statistically significant at the 95% confidence level
Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.
Estimations made using data from 25,000 runs for each landscape and ss-max condition. All runs used Small World II network, and parameters collab = 0.8 and recomb = 0.8.

3. Results by Environment

Table OA3. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by Environment and ss-max.
	Actor chooses max performing idea (ss-max = TRUE)								Actor chooses better performing idea (ss-max = FALSE)
	collab = 0.3 & recomb = 0.3		collab = 0.3 & recomb = 0.8		collab = 0.8 & recomb = 0.3		collab = 0.8 & recomb = 0.8		collab = 0.3 & recomb = 0.3		collab = 0.3 & recomb = 0.8		collab = 0.8 & recomb = 0.3		collab = 0.8 & recomb = 0.8
	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain activity	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
Within-network-community recombination	9.23	-6.58	4.08	-7.78	2.96	-11.71	1.94	-7.92	2.26	-11.17	1.98	-11.76	2.14	-4.35	0.61	-2.69
Between-network-community recombination	10.81	-5.14	3.98	-7.26	3.19	-12.49	2.66	-5.66	3.91	-9.07	2.02	-10.31	2.89	-5.70	1.10	-1.79
Within-network-community transfer	-0.01	1.55ns	-0.13	0.43	-0.07	1.84	-0.58	-0.03	-0.82	-1.16	-0.64	0.73	-0.25	-0.24	-0.41	0.56
Between-network-community transfer	-0.01	1.66	-0.12ns	0.90	0.07	6.68	0.21	3.53	-0.61	-0.28	-0.65	-0.79	0.01	3.05	-0.01	3.36
Self-search	-0.01	1.90	-0.19	1.19	-0.09	28.71	-1.21	16.77	-0.07	11.23	-0.27	11.07	0.23	9.78	-0.26	7.39
No. of observations (chains)	185,403	65,046	185,402	67,388	185,348	67,660	185,477	86,088	185,547	78,926	185,394	82,304	184,846	77,057	185,278	102,120
Notes:
nsEstimated coefficients are not statistically significant at the 95% confidence level
Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.
Estimations made using data from 250,000 runs for each environment and ss-max condition (25,000 runs by landscape). All runs used network Small World II.

4. Results by Partner Selection Process

Table OA4. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by partner selection process.
	Random partner selection		Performance based partner selection
	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain acivity	(1)	(2)	(3)	(4)
Within-network-community recombination	1.79	-8.51	2.16	-9.70
Between-network-community recombination	2.29	-5.98	2.69	-5.96
Within-network-community transfer	-0.69	0.62ns	-0.54	-0.48
Between-network-community transfer	0.47	4.68	0.06ns	6.66
Self-search	-1.09	17.05	-0.96	17.72
No. of observations (chains)	37,029	17,273	37,002	16,513
Notes:
nsEstimated coefficients are not statistically significant at the 95% confidence level.
'Performance based partner selection' results are based on a version of the model where ego only interacts with alters who are better performing. 'Random partner selection' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes.
Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.
Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.

5. Results by Initial Condition

Table OA5. Expected percentage point change in the probability of a given action chain reaching the last mile (Model 1) and developing into the best idea (Model 2) corresponding to one additional change activity, by initial condition.
	Actors starting outside the global basin		Actors starting at any location
	Model 1	Model 2	Model 1	Model 2
	Entered Last Mile	Reached Best Idea	Entered Last Mile	Reached Best Idea
Action chain acivity	(1)	(2)	(3)	(4)
Within-network-community recombination	1.79	-8.51	1.44	-6.00
Between-network-community recombination	2.29	-5.98	2.10	-3.51
Within-network-community transfer	-0.69	0.62ns	-0.40	-1.20
Between-network-community transfer	0.47	4.68	0.32ns	3.99
Self-search	-1.09	17.05	-0.89	16.96
No. of observations (chains)	37,029	17,273	36,596	17,769
Notes:
nsEstimated coefficients are not statistically significant at the 95% confidence level.
'Actors starting outside the global basin' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes. In said model, the centroid for the network community could not be a location from which an actor could find the global peak through only self-search. 'Actors starting at any location' results are based on a version of the model that relaxes that restriction.
Probability changes calculated for the median observation using logistic regressions. Model 1 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. Model 2 estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.
Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.